The task of estimating the support of a sparse signal based on noisy measurements plays a key role in many applications, such as, image denoising [1]}, [2]}, communication [3]}, machine learning [4]}, [5]}, [6]}. Here, we consider support recovery of an unknown ternary signal \({\mbox{$\theta $}}^* \in \left\lbrace -1,0,1\right\rbrace ^D\) , given the noisy vector
\( {\mbox{$y$}} = {\mbox{$X$}}{\mbox{$\theta $}}^* + {\mbox{$\omega $}},\) 
